Numerical Methods for Evaluating the Derivatives of Eigenvalues and Eigenvectors

Abstract

[[abstract]]The paper presents two numerical methods for computing the derivatives of eigenvalues and eigenvectors. The first is an iteration method for finding the first partial derivatives of the eigenvalues and eigenvectors of a self-adjoint system. The iteration method will also find the first partial derivative of the largest eigenvalue and its corresponding eigenvector of a nonself-adjoint system, but the method cannot be used to find the derivatives of the remaining n-1 eigenvalues and eigenvectors. The second method requires only one eigenvector to find all orders of its derivatives and the derivatives of its corresponding eigenvalue. The method requires the solution of n+1 simultaneous equations where n is the number of coordinates of an eigenvector (10 refs.)[[fileno]]2020419010001[[department]]工工